I wonder how to build a 1-1 correspondence between [0,1] and [0,1). My professor offers an example such that 1 in the first set corresponds to 1/2 in the second set, and 1/2 in the first set corresponds to 1/4 in the second. I don't quite understand it. Does it mean every element in the first set corresponds to its half value in the second set? wouldn't that make some elements left out in the second set? Does it still count as 1-1 correspondence? Does it connect to Schroder-Bernstein theorem?
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